Sure, let's break this problem down step-by-step:
1. Identify the Expression:
The given expression is:
[tex]\[
x^3 (2x + 5) - 4 (2x + 5)
\][/tex]
2. Find the Common Factor:
Notice that both terms in the expression share the common factor [tex]\( (2x + 5) \)[/tex]. This is the key aspect that allows us to factorize the expression.
3. Factor Out the Common Factor:
We can factor [tex]\( (2x + 5) \)[/tex] out of the expression:
[tex]\[
(2x + 5) \left( x^3 \right) - (2x + 5) \left( 4 \right)
\][/tex]
4. Group the Remaining Terms:
Once we've factored out [tex]\( (2x + 5) \)[/tex], we group the remaining terms inside parentheses:
[tex]\[
(2x + 5) \left( x^3 - 4 \right)
\][/tex]
This is the completely factored form of the given expression.
So, the factored form is:
[tex]\[
(2x + 5) (x^3 - 4)
\][/tex]
And the common factor in the terms is:
[tex]\[
2x + 5
\][/tex]
Hence, the modified expression [tex]\( x^3(2x + 5) - 4(2x + 5) \)[/tex] can be factored into:
[tex]\[
(2x + 5)(x^3 - 4)
\][/tex]
And the common factor in the original terms is:
[tex]\[
2x + 5
\][/tex]
